A particle with charge 3.01 µC on the negative x axis and a second particle with charge 6.02 µC on the positive x axis are each a distance 0.0429 m from the origin. Where should a third particle with charge 9.03 µC be placed so that the magnitude of the electric field at the origin is zero?

The third particle should be at 0.0743 m from the origin on the negative x-axis.

Explanation:

Let's assume that the third charge is on the negative x-axis. So we have:

We know that the electric field is:

Where:

So, we have:

Let's solve it for r(3).

Therefore, the third particle should be at 0.0743 m from the origin on the negative x-axis.

I hope it helps you!